The Sun says Hodgson wants £20million-rated World Cup star Asamoah Gyan as he begins building a new-look Liverpool team.
The Rennes striker emerged as one of the players of the tournament during Ghana's march to the quarter-finals.
The Dutch ace, 27, said: "The truth is I want to play football - I don't want to be just sitting on the bench - so we will see what happens."
And the third forward linked with Anfield is former Reds' favourite Peter Crouch.
The England man, 29, is now at Tottenham but enjoyed his spell on Merseyside, scoring 40 goals in three seasons.